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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 15 Jan 2013 20:15:35 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Jan/15/t1358298949muh5i6ajh8qwle7.htm/, Retrieved Sun, 28 Apr 2024 14:28:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205584, Retrieved Sun, 28 Apr 2024 14:28:33 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Exponential Smoothing] [] [2013-01-16 01:15:35] [f824ea295e177f9d3dd7528a75f4b680] [Current]

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Dataseries X:

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1,65
1,66
1,66
1,67
1,68
1,68
1,68
1,68
1,69
1,7
1,7
1,71
1,72
1,73
1,74
1,74
1,75
1,75
1,75
1,76
1,79
1,83
1,84
1,85
1,87
1,87
1,87
1,88
1,88
1,88
1,88
1,89
1,89
1,89
1,9
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,9
1,9
1,92
1,93
1,92
1,95
1,96
1,96
1,96
1,96
1,96
1,97
1,97
1,97
1,97
1,97
1,97

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205584&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205584&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205584&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.199660169567295
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.199660169567295 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205584&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.199660169567295[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205584&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205584&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.199660169567295
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.66	1.67	-0.01
4	1.67	1.66800339830433	0.00199660169567295
5	1.68	1.67840204013744	0.00159795986255662
6	1.68	1.68872108907456	-0.00872108907456326
7	1.68	1.68697983495112	-0.00697983495112453
8	1.68	1.68558623992123	-0.0055862399212312
9	1.69	1.68447089031131	0.00552910968868536
10	1.7	1.69557483328931	0.00442516671068627
11	1.7	1.70645836282513	-0.0064583628251329
12	1.71	1.70516888500834	0.00483111499166022
13	1.72	1.71613346624677	0.00386653375322621
14	1.73	1.72690545903158	0.00309454096841955
15	1.74	1.73752331560607	0.00247668439393189
16	1.74	1.74801781083213	-0.00801781083212516
17	1.75	1.74641697336182	0.00358302663817534
18	1.75	1.75713236106797	-0.00713236106796677
19	1.75	1.75570831264772	-0.00570831264772131
20	1.76	1.75456858997653	0.00543141002346581
21	1.79	1.76565302622281	0.0243469737771911
22	1.83	1.80051414713561	0.0294858528643867
23	1.84	1.84640129751835	-0.00640129751835317
24	1.85	1.85512321337039	-0.00512321337038801
25	1.87	1.86410031172013	0.00589968827987319
26	1.87	1.88527824448248	-0.0152782444824806
27	1.87	1.88222778759842	-0.0122277875984178
28	1.88	1.87978638545308	0.000213614546914931
29	1.88	1.88982903576974	-0.00982903576974392
30	1.88	1.88786656882127	-0.00786656882127379
31	1.88	1.88629592835651	-0.00629592835650561
32	1.89	1.88503888223326	0.00496111776673791
33	1.89	1.89602941984781	-0.00602941984781236
34	1.89	1.89482558485861	-0.00482558485860562
35	1.9	1.89386210776748	0.00613789223252481
36	1.89	1.90508760037141	-0.0150876003714069
37	1.89	1.89207520752289	-0.00207520752288826
38	1.89	1.89166087123698	-0.001660871236981
39	1.89	1.89132926140418	-0.001329261404176
40	1.89	1.89106386084682	-0.00106386084681898
41	1.89	1.89085145020975	-0.000851450209746973
42	1.89	1.89068144951649	-0.000681449516490851
43	1.89	1.89054539119048	-0.000545391190476696
44	1.89	1.89043649829291	-0.000436498292905707
45	1.89	1.89034934696973	-0.000349346969728215
46	1.89	1.89027959629451	-0.000279596294514572
47	1.89	1.89022377205094	-0.000223772050941262
48	1.89	1.89017909368531	-0.000179093685305887
49	1.89	1.89014333580973	-0.000143335809729361
50	1.89	1.89011471735765	-0.000114717357653671
51	1.89	1.89009181287057	-9.18128705722498e-05
52	1.89	1.89007348149727	-7.34814972653819e-05
53	1.89	1.89005881016906	-5.88101690612852e-05
54	1.89	1.89004706812073	-4.70681207342949e-05
55	1.89	1.89003767049177	-3.76704917672832e-05
56	1.9	1.89003014919499	0.00996985080500679
57	1.9	1.90202073129728	-0.00202073129728153
58	1.92	1.90161727174382	0.0183827282561837
59	1.93	1.92528757038456	0.0047124296154446
60	1.92	1.93622845488065	-0.0162284548806491
61	1.95	1.92298827882736	0.0270117211726366
62	1.96	1.958381443657	0.00161855634300334
63	1.96	1.96870460489089	-0.00870460489089497
64	1.96	1.96696664200236	-0.00696664200236241
65	1.96	1.96557568107886	-0.00557568107885609
66	1.96	1.9644624396492	-0.00446243964919857
67	1.97	1.96357146819216	0.00642853180784431
68	1.97	1.97485498994298	-0.00485498994297862
69	1.97	1.97388564182772	-0.003885641827716
70	1.97	1.97310983392152	-0.00310983392151654
71	1.97	1.97248892395342	-0.00248892395342049
72	1.97	1.97199198497484	-0.00199198497484043

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.66 & 1.67 & -0.01 \tabularnewline
4 & 1.67 & 1.66800339830433 & 0.00199660169567295 \tabularnewline
5 & 1.68 & 1.67840204013744 & 0.00159795986255662 \tabularnewline
6 & 1.68 & 1.68872108907456 & -0.00872108907456326 \tabularnewline
7 & 1.68 & 1.68697983495112 & -0.00697983495112453 \tabularnewline
8 & 1.68 & 1.68558623992123 & -0.0055862399212312 \tabularnewline
9 & 1.69 & 1.68447089031131 & 0.00552910968868536 \tabularnewline
10 & 1.7 & 1.69557483328931 & 0.00442516671068627 \tabularnewline
11 & 1.7 & 1.70645836282513 & -0.0064583628251329 \tabularnewline
12 & 1.71 & 1.70516888500834 & 0.00483111499166022 \tabularnewline
13 & 1.72 & 1.71613346624677 & 0.00386653375322621 \tabularnewline
14 & 1.73 & 1.72690545903158 & 0.00309454096841955 \tabularnewline
15 & 1.74 & 1.73752331560607 & 0.00247668439393189 \tabularnewline
16 & 1.74 & 1.74801781083213 & -0.00801781083212516 \tabularnewline
17 & 1.75 & 1.74641697336182 & 0.00358302663817534 \tabularnewline
18 & 1.75 & 1.75713236106797 & -0.00713236106796677 \tabularnewline
19 & 1.75 & 1.75570831264772 & -0.00570831264772131 \tabularnewline
20 & 1.76 & 1.75456858997653 & 0.00543141002346581 \tabularnewline
21 & 1.79 & 1.76565302622281 & 0.0243469737771911 \tabularnewline
22 & 1.83 & 1.80051414713561 & 0.0294858528643867 \tabularnewline
23 & 1.84 & 1.84640129751835 & -0.00640129751835317 \tabularnewline
24 & 1.85 & 1.85512321337039 & -0.00512321337038801 \tabularnewline
25 & 1.87 & 1.86410031172013 & 0.00589968827987319 \tabularnewline
26 & 1.87 & 1.88527824448248 & -0.0152782444824806 \tabularnewline
27 & 1.87 & 1.88222778759842 & -0.0122277875984178 \tabularnewline
28 & 1.88 & 1.87978638545308 & 0.000213614546914931 \tabularnewline
29 & 1.88 & 1.88982903576974 & -0.00982903576974392 \tabularnewline
30 & 1.88 & 1.88786656882127 & -0.00786656882127379 \tabularnewline
31 & 1.88 & 1.88629592835651 & -0.00629592835650561 \tabularnewline
32 & 1.89 & 1.88503888223326 & 0.00496111776673791 \tabularnewline
33 & 1.89 & 1.89602941984781 & -0.00602941984781236 \tabularnewline
34 & 1.89 & 1.89482558485861 & -0.00482558485860562 \tabularnewline
35 & 1.9 & 1.89386210776748 & 0.00613789223252481 \tabularnewline
36 & 1.89 & 1.90508760037141 & -0.0150876003714069 \tabularnewline
37 & 1.89 & 1.89207520752289 & -0.00207520752288826 \tabularnewline
38 & 1.89 & 1.89166087123698 & -0.001660871236981 \tabularnewline
39 & 1.89 & 1.89132926140418 & -0.001329261404176 \tabularnewline
40 & 1.89 & 1.89106386084682 & -0.00106386084681898 \tabularnewline
41 & 1.89 & 1.89085145020975 & -0.000851450209746973 \tabularnewline
42 & 1.89 & 1.89068144951649 & -0.000681449516490851 \tabularnewline
43 & 1.89 & 1.89054539119048 & -0.000545391190476696 \tabularnewline
44 & 1.89 & 1.89043649829291 & -0.000436498292905707 \tabularnewline
45 & 1.89 & 1.89034934696973 & -0.000349346969728215 \tabularnewline
46 & 1.89 & 1.89027959629451 & -0.000279596294514572 \tabularnewline
47 & 1.89 & 1.89022377205094 & -0.000223772050941262 \tabularnewline
48 & 1.89 & 1.89017909368531 & -0.000179093685305887 \tabularnewline
49 & 1.89 & 1.89014333580973 & -0.000143335809729361 \tabularnewline
50 & 1.89 & 1.89011471735765 & -0.000114717357653671 \tabularnewline
51 & 1.89 & 1.89009181287057 & -9.18128705722498e-05 \tabularnewline
52 & 1.89 & 1.89007348149727 & -7.34814972653819e-05 \tabularnewline
53 & 1.89 & 1.89005881016906 & -5.88101690612852e-05 \tabularnewline
54 & 1.89 & 1.89004706812073 & -4.70681207342949e-05 \tabularnewline
55 & 1.89 & 1.89003767049177 & -3.76704917672832e-05 \tabularnewline
56 & 1.9 & 1.89003014919499 & 0.00996985080500679 \tabularnewline
57 & 1.9 & 1.90202073129728 & -0.00202073129728153 \tabularnewline
58 & 1.92 & 1.90161727174382 & 0.0183827282561837 \tabularnewline
59 & 1.93 & 1.92528757038456 & 0.0047124296154446 \tabularnewline
60 & 1.92 & 1.93622845488065 & -0.0162284548806491 \tabularnewline
61 & 1.95 & 1.92298827882736 & 0.0270117211726366 \tabularnewline
62 & 1.96 & 1.958381443657 & 0.00161855634300334 \tabularnewline
63 & 1.96 & 1.96870460489089 & -0.00870460489089497 \tabularnewline
64 & 1.96 & 1.96696664200236 & -0.00696664200236241 \tabularnewline
65 & 1.96 & 1.96557568107886 & -0.00557568107885609 \tabularnewline
66 & 1.96 & 1.9644624396492 & -0.00446243964919857 \tabularnewline
67 & 1.97 & 1.96357146819216 & 0.00642853180784431 \tabularnewline
68 & 1.97 & 1.97485498994298 & -0.00485498994297862 \tabularnewline
69 & 1.97 & 1.97388564182772 & -0.003885641827716 \tabularnewline
70 & 1.97 & 1.97310983392152 & -0.00310983392151654 \tabularnewline
71 & 1.97 & 1.97248892395342 & -0.00248892395342049 \tabularnewline
72 & 1.97 & 1.97199198497484 & -0.00199198497484043 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205584&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]1.66[/C][C]1.67[/C][C]-0.01[/C][/ROW]
[ROW][C]4[/C][C]1.67[/C][C]1.66800339830433[/C][C]0.00199660169567295[/C][/ROW]
[ROW][C]5[/C][C]1.68[/C][C]1.67840204013744[/C][C]0.00159795986255662[/C][/ROW]
[ROW][C]6[/C][C]1.68[/C][C]1.68872108907456[/C][C]-0.00872108907456326[/C][/ROW]
[ROW][C]7[/C][C]1.68[/C][C]1.68697983495112[/C][C]-0.00697983495112453[/C][/ROW]
[ROW][C]8[/C][C]1.68[/C][C]1.68558623992123[/C][C]-0.0055862399212312[/C][/ROW]
[ROW][C]9[/C][C]1.69[/C][C]1.68447089031131[/C][C]0.00552910968868536[/C][/ROW]
[ROW][C]10[/C][C]1.7[/C][C]1.69557483328931[/C][C]0.00442516671068627[/C][/ROW]
[ROW][C]11[/C][C]1.7[/C][C]1.70645836282513[/C][C]-0.0064583628251329[/C][/ROW]
[ROW][C]12[/C][C]1.71[/C][C]1.70516888500834[/C][C]0.00483111499166022[/C][/ROW]
[ROW][C]13[/C][C]1.72[/C][C]1.71613346624677[/C][C]0.00386653375322621[/C][/ROW]
[ROW][C]14[/C][C]1.73[/C][C]1.72690545903158[/C][C]0.00309454096841955[/C][/ROW]
[ROW][C]15[/C][C]1.74[/C][C]1.73752331560607[/C][C]0.00247668439393189[/C][/ROW]
[ROW][C]16[/C][C]1.74[/C][C]1.74801781083213[/C][C]-0.00801781083212516[/C][/ROW]
[ROW][C]17[/C][C]1.75[/C][C]1.74641697336182[/C][C]0.00358302663817534[/C][/ROW]
[ROW][C]18[/C][C]1.75[/C][C]1.75713236106797[/C][C]-0.00713236106796677[/C][/ROW]
[ROW][C]19[/C][C]1.75[/C][C]1.75570831264772[/C][C]-0.00570831264772131[/C][/ROW]
[ROW][C]20[/C][C]1.76[/C][C]1.75456858997653[/C][C]0.00543141002346581[/C][/ROW]
[ROW][C]21[/C][C]1.79[/C][C]1.76565302622281[/C][C]0.0243469737771911[/C][/ROW]
[ROW][C]22[/C][C]1.83[/C][C]1.80051414713561[/C][C]0.0294858528643867[/C][/ROW]
[ROW][C]23[/C][C]1.84[/C][C]1.84640129751835[/C][C]-0.00640129751835317[/C][/ROW]
[ROW][C]24[/C][C]1.85[/C][C]1.85512321337039[/C][C]-0.00512321337038801[/C][/ROW]
[ROW][C]25[/C][C]1.87[/C][C]1.86410031172013[/C][C]0.00589968827987319[/C][/ROW]
[ROW][C]26[/C][C]1.87[/C][C]1.88527824448248[/C][C]-0.0152782444824806[/C][/ROW]
[ROW][C]27[/C][C]1.87[/C][C]1.88222778759842[/C][C]-0.0122277875984178[/C][/ROW]
[ROW][C]28[/C][C]1.88[/C][C]1.87978638545308[/C][C]0.000213614546914931[/C][/ROW]
[ROW][C]29[/C][C]1.88[/C][C]1.88982903576974[/C][C]-0.00982903576974392[/C][/ROW]
[ROW][C]30[/C][C]1.88[/C][C]1.88786656882127[/C][C]-0.00786656882127379[/C][/ROW]
[ROW][C]31[/C][C]1.88[/C][C]1.88629592835651[/C][C]-0.00629592835650561[/C][/ROW]
[ROW][C]32[/C][C]1.89[/C][C]1.88503888223326[/C][C]0.00496111776673791[/C][/ROW]
[ROW][C]33[/C][C]1.89[/C][C]1.89602941984781[/C][C]-0.00602941984781236[/C][/ROW]
[ROW][C]34[/C][C]1.89[/C][C]1.89482558485861[/C][C]-0.00482558485860562[/C][/ROW]
[ROW][C]35[/C][C]1.9[/C][C]1.89386210776748[/C][C]0.00613789223252481[/C][/ROW]
[ROW][C]36[/C][C]1.89[/C][C]1.90508760037141[/C][C]-0.0150876003714069[/C][/ROW]
[ROW][C]37[/C][C]1.89[/C][C]1.89207520752289[/C][C]-0.00207520752288826[/C][/ROW]
[ROW][C]38[/C][C]1.89[/C][C]1.89166087123698[/C][C]-0.001660871236981[/C][/ROW]
[ROW][C]39[/C][C]1.89[/C][C]1.89132926140418[/C][C]-0.001329261404176[/C][/ROW]
[ROW][C]40[/C][C]1.89[/C][C]1.89106386084682[/C][C]-0.00106386084681898[/C][/ROW]
[ROW][C]41[/C][C]1.89[/C][C]1.89085145020975[/C][C]-0.000851450209746973[/C][/ROW]
[ROW][C]42[/C][C]1.89[/C][C]1.89068144951649[/C][C]-0.000681449516490851[/C][/ROW]
[ROW][C]43[/C][C]1.89[/C][C]1.89054539119048[/C][C]-0.000545391190476696[/C][/ROW]
[ROW][C]44[/C][C]1.89[/C][C]1.89043649829291[/C][C]-0.000436498292905707[/C][/ROW]
[ROW][C]45[/C][C]1.89[/C][C]1.89034934696973[/C][C]-0.000349346969728215[/C][/ROW]
[ROW][C]46[/C][C]1.89[/C][C]1.89027959629451[/C][C]-0.000279596294514572[/C][/ROW]
[ROW][C]47[/C][C]1.89[/C][C]1.89022377205094[/C][C]-0.000223772050941262[/C][/ROW]
[ROW][C]48[/C][C]1.89[/C][C]1.89017909368531[/C][C]-0.000179093685305887[/C][/ROW]
[ROW][C]49[/C][C]1.89[/C][C]1.89014333580973[/C][C]-0.000143335809729361[/C][/ROW]
[ROW][C]50[/C][C]1.89[/C][C]1.89011471735765[/C][C]-0.000114717357653671[/C][/ROW]
[ROW][C]51[/C][C]1.89[/C][C]1.89009181287057[/C][C]-9.18128705722498e-05[/C][/ROW]
[ROW][C]52[/C][C]1.89[/C][C]1.89007348149727[/C][C]-7.34814972653819e-05[/C][/ROW]
[ROW][C]53[/C][C]1.89[/C][C]1.89005881016906[/C][C]-5.88101690612852e-05[/C][/ROW]
[ROW][C]54[/C][C]1.89[/C][C]1.89004706812073[/C][C]-4.70681207342949e-05[/C][/ROW]
[ROW][C]55[/C][C]1.89[/C][C]1.89003767049177[/C][C]-3.76704917672832e-05[/C][/ROW]
[ROW][C]56[/C][C]1.9[/C][C]1.89003014919499[/C][C]0.00996985080500679[/C][/ROW]
[ROW][C]57[/C][C]1.9[/C][C]1.90202073129728[/C][C]-0.00202073129728153[/C][/ROW]
[ROW][C]58[/C][C]1.92[/C][C]1.90161727174382[/C][C]0.0183827282561837[/C][/ROW]
[ROW][C]59[/C][C]1.93[/C][C]1.92528757038456[/C][C]0.0047124296154446[/C][/ROW]
[ROW][C]60[/C][C]1.92[/C][C]1.93622845488065[/C][C]-0.0162284548806491[/C][/ROW]
[ROW][C]61[/C][C]1.95[/C][C]1.92298827882736[/C][C]0.0270117211726366[/C][/ROW]
[ROW][C]62[/C][C]1.96[/C][C]1.958381443657[/C][C]0.00161855634300334[/C][/ROW]
[ROW][C]63[/C][C]1.96[/C][C]1.96870460489089[/C][C]-0.00870460489089497[/C][/ROW]
[ROW][C]64[/C][C]1.96[/C][C]1.96696664200236[/C][C]-0.00696664200236241[/C][/ROW]
[ROW][C]65[/C][C]1.96[/C][C]1.96557568107886[/C][C]-0.00557568107885609[/C][/ROW]
[ROW][C]66[/C][C]1.96[/C][C]1.9644624396492[/C][C]-0.00446243964919857[/C][/ROW]
[ROW][C]67[/C][C]1.97[/C][C]1.96357146819216[/C][C]0.00642853180784431[/C][/ROW]
[ROW][C]68[/C][C]1.97[/C][C]1.97485498994298[/C][C]-0.00485498994297862[/C][/ROW]
[ROW][C]69[/C][C]1.97[/C][C]1.97388564182772[/C][C]-0.003885641827716[/C][/ROW]
[ROW][C]70[/C][C]1.97[/C][C]1.97310983392152[/C][C]-0.00310983392151654[/C][/ROW]
[ROW][C]71[/C][C]1.97[/C][C]1.97248892395342[/C][C]-0.00248892395342049[/C][/ROW]
[ROW][C]72[/C][C]1.97[/C][C]1.97199198497484[/C][C]-0.00199198497484043[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205584&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205584&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.66	1.67	-0.01
4	1.67	1.66800339830433	0.00199660169567295
5	1.68	1.67840204013744	0.00159795986255662
6	1.68	1.68872108907456	-0.00872108907456326
7	1.68	1.68697983495112	-0.00697983495112453
8	1.68	1.68558623992123	-0.0055862399212312
9	1.69	1.68447089031131	0.00552910968868536
10	1.7	1.69557483328931	0.00442516671068627
11	1.7	1.70645836282513	-0.0064583628251329
12	1.71	1.70516888500834	0.00483111499166022
13	1.72	1.71613346624677	0.00386653375322621
14	1.73	1.72690545903158	0.00309454096841955
15	1.74	1.73752331560607	0.00247668439393189
16	1.74	1.74801781083213	-0.00801781083212516
17	1.75	1.74641697336182	0.00358302663817534
18	1.75	1.75713236106797	-0.00713236106796677
19	1.75	1.75570831264772	-0.00570831264772131
20	1.76	1.75456858997653	0.00543141002346581
21	1.79	1.76565302622281	0.0243469737771911
22	1.83	1.80051414713561	0.0294858528643867
23	1.84	1.84640129751835	-0.00640129751835317
24	1.85	1.85512321337039	-0.00512321337038801
25	1.87	1.86410031172013	0.00589968827987319
26	1.87	1.88527824448248	-0.0152782444824806
27	1.87	1.88222778759842	-0.0122277875984178
28	1.88	1.87978638545308	0.000213614546914931
29	1.88	1.88982903576974	-0.00982903576974392
30	1.88	1.88786656882127	-0.00786656882127379
31	1.88	1.88629592835651	-0.00629592835650561
32	1.89	1.88503888223326	0.00496111776673791
33	1.89	1.89602941984781	-0.00602941984781236
34	1.89	1.89482558485861	-0.00482558485860562
35	1.9	1.89386210776748	0.00613789223252481
36	1.89	1.90508760037141	-0.0150876003714069
37	1.89	1.89207520752289	-0.00207520752288826
38	1.89	1.89166087123698	-0.001660871236981
39	1.89	1.89132926140418	-0.001329261404176
40	1.89	1.89106386084682	-0.00106386084681898
41	1.89	1.89085145020975	-0.000851450209746973
42	1.89	1.89068144951649	-0.000681449516490851
43	1.89	1.89054539119048	-0.000545391190476696
44	1.89	1.89043649829291	-0.000436498292905707
45	1.89	1.89034934696973	-0.000349346969728215
46	1.89	1.89027959629451	-0.000279596294514572
47	1.89	1.89022377205094	-0.000223772050941262
48	1.89	1.89017909368531	-0.000179093685305887
49	1.89	1.89014333580973	-0.000143335809729361
50	1.89	1.89011471735765	-0.000114717357653671
51	1.89	1.89009181287057	-9.18128705722498e-05
52	1.89	1.89007348149727	-7.34814972653819e-05
53	1.89	1.89005881016906	-5.88101690612852e-05
54	1.89	1.89004706812073	-4.70681207342949e-05
55	1.89	1.89003767049177	-3.76704917672832e-05
56	1.9	1.89003014919499	0.00996985080500679
57	1.9	1.90202073129728	-0.00202073129728153
58	1.92	1.90161727174382	0.0183827282561837
59	1.93	1.92528757038456	0.0047124296154446
60	1.92	1.93622845488065	-0.0162284548806491
61	1.95	1.92298827882736	0.0270117211726366
62	1.96	1.958381443657	0.00161855634300334
63	1.96	1.96870460489089	-0.00870460489089497
64	1.96	1.96696664200236	-0.00696664200236241
65	1.96	1.96557568107886	-0.00557568107885609
66	1.96	1.9644624396492	-0.00446243964919857
67	1.97	1.96357146819216	0.00642853180784431
68	1.97	1.97485498994298	-0.00485498994297862
69	1.97	1.97388564182772	-0.003885641827716
70	1.97	1.97310983392152	-0.00310983392151654
71	1.97	1.97248892395342	-0.00248892395342049
72	1.97	1.97199198497484	-0.00199198497484043

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.97159426491699	1.95522255174225	1.98796597809173
74	1.97318852983398	1.9476193701633	1.99875768950465
75	1.97478279475096	1.94045180824255	2.00911378125938
76	1.97637705966795	1.93320407100512	2.01955004833078
77	1.97797132458494	1.92571213682567	2.03023051234421
78	1.97956558950193	1.91791063241938	2.04122054658448
79	1.98115985441892	1.90977211131457	2.05254759752326
80	1.98275411933591	1.90128620579948	2.06422203287233
81	1.98434838425289	1.89245095895238	2.07624580955341
82	1.98594264916988	1.88326876144343	2.08861653689633
83	1.98753691408687	1.87374428646691	2.10132954170683
84	1.98913117900386	1.86388337962634	2.11437897838138

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.97159426491699 & 1.95522255174225 & 1.98796597809173 \tabularnewline
74 & 1.97318852983398 & 1.9476193701633 & 1.99875768950465 \tabularnewline
75 & 1.97478279475096 & 1.94045180824255 & 2.00911378125938 \tabularnewline
76 & 1.97637705966795 & 1.93320407100512 & 2.01955004833078 \tabularnewline
77 & 1.97797132458494 & 1.92571213682567 & 2.03023051234421 \tabularnewline
78 & 1.97956558950193 & 1.91791063241938 & 2.04122054658448 \tabularnewline
79 & 1.98115985441892 & 1.90977211131457 & 2.05254759752326 \tabularnewline
80 & 1.98275411933591 & 1.90128620579948 & 2.06422203287233 \tabularnewline
81 & 1.98434838425289 & 1.89245095895238 & 2.07624580955341 \tabularnewline
82 & 1.98594264916988 & 1.88326876144343 & 2.08861653689633 \tabularnewline
83 & 1.98753691408687 & 1.87374428646691 & 2.10132954170683 \tabularnewline
84 & 1.98913117900386 & 1.86388337962634 & 2.11437897838138 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205584&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]1.97159426491699[/C][C]1.95522255174225[/C][C]1.98796597809173[/C][/ROW]
[ROW][C]74[/C][C]1.97318852983398[/C][C]1.9476193701633[/C][C]1.99875768950465[/C][/ROW]
[ROW][C]75[/C][C]1.97478279475096[/C][C]1.94045180824255[/C][C]2.00911378125938[/C][/ROW]
[ROW][C]76[/C][C]1.97637705966795[/C][C]1.93320407100512[/C][C]2.01955004833078[/C][/ROW]
[ROW][C]77[/C][C]1.97797132458494[/C][C]1.92571213682567[/C][C]2.03023051234421[/C][/ROW]
[ROW][C]78[/C][C]1.97956558950193[/C][C]1.91791063241938[/C][C]2.04122054658448[/C][/ROW]
[ROW][C]79[/C][C]1.98115985441892[/C][C]1.90977211131457[/C][C]2.05254759752326[/C][/ROW]
[ROW][C]80[/C][C]1.98275411933591[/C][C]1.90128620579948[/C][C]2.06422203287233[/C][/ROW]
[ROW][C]81[/C][C]1.98434838425289[/C][C]1.89245095895238[/C][C]2.07624580955341[/C][/ROW]
[ROW][C]82[/C][C]1.98594264916988[/C][C]1.88326876144343[/C][C]2.08861653689633[/C][/ROW]
[ROW][C]83[/C][C]1.98753691408687[/C][C]1.87374428646691[/C][C]2.10132954170683[/C][/ROW]
[ROW][C]84[/C][C]1.98913117900386[/C][C]1.86388337962634[/C][C]2.11437897838138[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205584&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205584&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.97159426491699	1.95522255174225	1.98796597809173
74	1.97318852983398	1.9476193701633	1.99875768950465
75	1.97478279475096	1.94045180824255	2.00911378125938
76	1.97637705966795	1.93320407100512	2.01955004833078
77	1.97797132458494	1.92571213682567	2.03023051234421
78	1.97956558950193	1.91791063241938	2.04122054658448
79	1.98115985441892	1.90977211131457	2.05254759752326
80	1.98275411933591	1.90128620579948	2.06422203287233
81	1.98434838425289	1.89245095895238	2.07624580955341
82	1.98594264916988	1.88326876144343	2.08861653689633
83	1.98753691408687	1.87374428646691	2.10132954170683
84	1.98913117900386	1.86388337962634	2.11437897838138

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = additive ; par2 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code